Phase retrieval from the FTIR transmittance spectrum of thick materials with anchoring points in THz-TDS measurement

Extraction of the refractive index for optically thick and low-loss materials with a single Fourier transform infrared spectrometer (FTIR) transmittance spectrum becomes difficult with the conventional root-finding method at THz frequencies. A phase-retrieval method was proposed based on Kramers-Kronig (K-K) relations with anchoring points from independently measured transmission data in THz-TDS. Two approaches, i.e., multiply subtractive K-K relations and fast Fourier transform, were utilized to successfully obtain the phase spectrum for 3.52 mm TPX and 1.08 mm crystal quartz with two and three anchoring points, respectively. The results agree with the phase from TDS in the overlapped frequency range from 1.5 to 4.5 THz. An iterative optimization algorithm was finally employed to extract the refractive index of the two materials with amplitude and retrieved the phase spectrum of the transmitted signal within the FTIR measured frequency range.